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Logical expression Let a, b, c E {0, 1} be bits. That is, cach of a, b, and c is either 0 or 1. For this problem, we equate false with 0 and true with 1. Let ø be a logical expression $ = (? V ?) ^ (c V ?) ^ (b v ?). We also write o as ø(a, b, c) since it is a function of the values assigned to the three variables a, b, and c. The formula o contains six terms in total. Two of the six terms are prc-filled. The third term is c, and the fifth term is b, the negation of b. The four remaining terms are cach one of {a,ā,b, b, c,c}. We want the formula o to take the values listed in the following truth table. a 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1. Find a way to set the four remaining terms in ø so that the formula o takes the values in the above truth table.

Logical expression Let a, b, c E {0, 1} be bits. That is, cach of a, b, and c is either 0 or 1. For this problem, we equate false with 0 and true with 1. Let ø be a logical expression $ = (? V ?) ^ (c V ?) ^ (b v ?). We also write o as ø(a, b, c) since it is a function of the values assigned to the three variables a, b, and c. The formula o contains six terms in total. Two of the six terms are prc-filled. The third term is c, and the fifth term is b, the negation of b. The four remaining terms are cach one of {a,ā,b, b, c,c}. We want the formula o to take the values listed in the following truth table. a 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1. Find a way to set the four remaining terms in ø so that the formula o takes the values in the above truth table.

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Logical Expression

Logical expression Let a, b, c € {0, 1} be bits. That is, cach of a, b, and c is either 0 or 1. For this problem, we equate false with 0 and true with 1. Let ø be a logical expression $ = (? V ?) ^ (c V ?) ^ (6 V ?). We also write o as o(a, b, c) since it is a function of the values assigned to the three variables a, b, and c. The formula o contains six terms in total. Two of the six terms are pre-filled. The third term is c, and the fifth term is 6, the negation of b. The four remaining terms are cach one of {a,ā, b, b, c, c}. We want the formula Ø to take the values listed in the following truth table. 1 1 1 1 1 1 0| 0 1 1 1 1 1 1 1 1 10 1. Find a way to set the four remaining terms in ø so that the formula o takes the values in the above truth table. At the beginning of your submission, give a table as shown here, and put one of {a, ā, b, b, c, t} in cach box, indicating your answer. 1 2 4 Succinctly explain your methodology and justify your answer. 2. Let 0 = (a → b) ^ (c→ b) ^ (ūÐ c). Give the truth table for 0. Show your calculations and justify. Give an interpretation of 0 in plain English. What does 0 compute? Explain.
Transcribed Image Text:Logical expression Let a, b, c € {0, 1} be bits. That is, cach of a, b, and c is either 0 or 1. For this problem, we equate false with 0 and true with 1. Let ø be a logical expression $ = (? V ?) ^ (c V ?) ^ (6 V ?). We also write o as o(a, b, c) since it is a function of the values assigned to the three variables a, b, and c. The formula o contains six terms in total. Two of the six terms are pre-filled. The third term is c, and the fifth term is 6, the negation of b. The four remaining terms are cach one of {a,ā, b, b, c, c}. We want the formula Ø to take the values listed in the following truth table. 1 1 1 1 1 1 0| 0 1 1 1 1 1 1 1 1 10 1. Find a way to set the four remaining terms in ø so that the formula o takes the values in the above truth table. At the beginning of your submission, give a table as shown here, and put one of {a, ā, b, b, c, t} in cach box, indicating your answer. 1 2 4 Succinctly explain your methodology and justify your answer. 2. Let 0 = (a → b) ^ (c→ b) ^ (ūÐ c). Give the truth table for 0. Show your calculations and justify. Give an interpretation of 0 in plain English. What does 0 compute? Explain.
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